Numbers that can be expressed in the form ,where p and q are integers and q≠0, are known as rational numbers. The collectionofrational numbers is denoted by Q. These rational numbers satisfies various laws or properties that are listed below:

Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number, then we say that rational numbers satisfy the closure law.

Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:

Commutative law under addition: a+b = b+aCommutative law under multiplication: axb = bxa

Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:

Associative law under addition: a+(b+c) = (a+b)+cAssociative law under multiplication: a(bc) = (ab)c

0 is the additive identity for rational numbers.

1 is the multiplicative identity for rational numbers.

The additive inverse of a is , and the additive inverse of .

If , then is the reciprocal or multiplicativeinverse of , and vice versa.

For all rational numbers, p, q and r, and , is known as thedistributiveproperty.

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